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On discrete Gibbs measure approximation to runs

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  • A. N. Kumar
  • N. S. Upadhye

Abstract

A Stein operator for the runs is derived as a perturbation of an operator for discrete Gibbs measure. Due to this fact, using perturbation technique, the approximation results for runs arising from identical and non-identical Bernoulli trials are derived via Stein’s method. The bounds obtained are new and their importance is demonstrated through an interesting application.

Suggested Citation

  • A. N. Kumar & N. S. Upadhye, 2022. "On discrete Gibbs measure approximation to runs," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(5), pages 1488-1513, March.
    • Handle: RePEc:taf:lstaxx:v:51:y:2022:i:5:p:1488-1513
    DOI: 10.1080/03610926.2020.1765256
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    Cited by:

    1. Waleed Ahmed Hassen Al-Nuaami & Ali Akbar Heydari & Hossein Jabbari Khamnei, 2023. "The Poisson–Lindley Distribution: Some Characteristics, with Its Application to SPC," Mathematics, MDPI, vol. 11(11), pages 1-16, May.
    2. Kumar, Amit N. & Kumar, Poleen, 2024. "A negative binomial approximation to the distribution of the sum of maxima of indicator random variables," Statistics & Probability Letters, Elsevier, vol. 208(C).

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